Punctual Hilbert schemes of points of \mathbbA³ in the Grothendieck group of varieties

2022/08/04 by Zhan, Sailun
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.02419

Abstract

We give an explicit stratification of the punctual Hilbert schemes of n points of \mathbbA^m+1 with respect to m-dimensional partitions in the Grothendieck group of varieties. As an application, we calculate the classes of the punctual Hilbert schemes of n points of \mathbbA³ and the classes of the Hilbert schemes of n points of \mathbbA³ in the Grothendieck of varieties for n≤ 5.

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